Question

Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points, to the nearest tenth (if necessary). (2,6) and (7,6) A) 144 B) 81 C) 89 D) 15

Answer 1

`D)15`

Step-by-step explanation

We want to find the distance between the two points given: (2, -6) and (-7, 6)

To do that, we will apply the formula for distance between two points:

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

where (x₁, y₁) and (x₂, y₂) are the two points.

We have that:

`\begin{gathered} \mleft(x_(1),y_(1)\mright)=(2,-6) \\ (x_2,y_2)=(-7,6) \end{gathered}`

Therefore, the distance between them is:

`\begin{gathered} d=\sqrt[]{(-7-2)^2+(6-(-6))^2}=\sqrt[]{(-9)^2_{}+(6+6)^2} \\ d=\sqrt[]{(-9)^2+(12)^2}=\sqrt[]{81+144} \\ d=\sqrt[]{225} \\ d=15 \end{gathered}`

That is the distance between the two points.